College Math

College Math Study Guide

outcomes. For instance, for tossing the coin, the sample space represented by S, would be written as S = {H, T}, where H means heads and T means tails. An event of the experiment is the subset of the sample space. For instance, suppose we toss one coin two times, then we generate the following sample space: S = {HT, HH, TH, TT} Now, the event of exactly one head would be E = {HT, TH}. Similarly, the event of no tails would be F = {HH} And so on… Now, let us discuss probability. Probability can be defined as the likelihood for any event to occur. For instance, in the above example of tossing a coin twice, if we say “what is the probability of getting exactly one head” means we are talking about probability. Given that S is the sample space of the experiment in which all the outcomes are equally likely, then the probability of an event E would be calculated as: ( ) = = ( ) ( ) In the above example, the probability of getting exactly one head would be: ( ) = = 2 4 = 0.5 It should be noted that n(E) ≥ 0 and n(S) ≥ n(E). Therefore, when n(E) = 0 then probability will be 0 and when n(S) = n(E), then probability will be equal to 1. Hence, the value of probability will always be between 0 and 1. Let us solve a few examples to understand the concept well. Suppose we draw four cards from a deck of 52 cards. What is the probability of drawing four hearts? The sample space will comprise of drawing 4 cards out of 52, which will be calculated using combination. C (52, 4) = 270725 = n(S) Now, we know that there are a total of 13 cards each of hearts, club, spades and diamond. Thus, drawing 4 cards out of 13 cards of hearts will be calculated by using the combination. C (13, 4) = 715 = n(E) Hence, the required probability will become. P(E) = n(E)/n(S) = 715/270725 = 0.0026

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